# internal libraries
import os
import warnings
from math import sqrt


# external libraries
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import plotly.offline
import plotly.express as px
import plotly.graph_objects as go
import plotly.subplots as sp 
import missingno as msno
from statsmodels.tsa.seasonal import seasonal_decompose, DecomposeResult
from statsmodels.stats.stattools import durbin_watson
from statsmodels.tsa.stattools import acf, pacf
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.stattools import adfuller
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import MinMaxScaler
from keras.models import Sequential
from keras.layers import Dense, LSTM
from keras.optimizers import Adam
from keras.callbacks import EarlyStopping
from keras.utils import plot_model

# Set project environment

FILE_PATH = os.getcwd() + "/data/AMZN.csv"

plotly.offline.init_notebook_mode()
warnings.filterwarnings("ignore")

# Load data and set date as index
def load_data():
    df = pd.read_csv(FILE_PATH, sep=',',decimal='.', index_col='Date', parse_dates=True)

    # lowercase column names
    df.columns = [col.lower() for col in df.columns]

    return df

df = load_data()

df.tail()

df.info()

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 6732 entries, 1997-05-15 to 2024-02-14
Data columns (total 6 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   open       6732 non-null   float64
 1   high       6732 non-null   float64
 2   low        6732 non-null   float64
 3   close      6732 non-null   float64
 4   adj close  6732 non-null   float64
 5   volume     6732 non-null   int64  
dtypes: float64(5), int64(1)
memory usage: 368.2 KB

def plot_stock_price(df: pd.DataFrame):

    fig = go.Figure( 
        data=[
            go.Candlestick(
                x=df.index,
                open=df["open"],
                high=df["high"],
                low=df["low"],
                close=df["close"],
            )
        ]
    )

    fig.update_layout(
        title="Amazon Stock Price",
        yaxis_title="Price",
        xaxis_title="Date",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
    )

    fig.show()

plot_stock_price(df.copy())

# plot the daily returns

def plot_daily_returns(df: pd.DataFrame):
    df['daily_returns'] = df['adj close'].pct_change(fill_method=None) # type: ignore

    fig = px.line(df, x=df.index, y="daily_returns", title='Daily Returns of Amazon Stock Price', labels={'daily_returns': 'Daily Returns', 'index': 'Date'})
    fig.show()

plot_daily_returns(df.copy())

# plot the daily returns as a histogram and calculate the mean and standard deviation of the daily returns 

def plot_daily_returns_histogram(df: pd.DataFrame):
    df['daily_returns'] = df['adj close'].pct_change(fill_method=None) # type: ignore

    fig = px.histogram(df, x="daily_returns", title='Daily Returns of Amazon Stock Price', labels={'daily_returns': 'Daily Returns', 'index': 'Date'})

    mean = df['daily_returns'].mean()
    std = df['daily_returns'].std()

    fig.update_layout(
        title="Amazon Stock Price Daily Returns Histogram",
        yaxis_title="Count",
        xaxis_title="Daily Returns",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
        legend_title_text=f"Mean: {str(np.round(mean, 4))} Std: {str(np.round(std, 4))}"
    )

    fig.add_trace(go.Scatter(x=[mean, mean], y=[0, 800], mode="lines", name="Mean"))
    fig.add_trace(go.Scatter(x=[mean + std, mean + std], y=[0, 800], mode="lines", name="Std"))
    fig.add_trace(go.Scatter(x=[mean - std, mean - std], y=[0, 800], mode="lines", name="Std"))
    fig.add_trace(go.Scatter(x=[mean + 2 * std, mean + 2 * std], y=[0, 800], mode="lines", name="2*Std"))
    fig.add_trace(go.Scatter(x=[mean - 2 * std, mean - 2 * std], y=[0, 800], mode="lines", name="2*Std"))

    fig.show()

plot_daily_returns_histogram(df.copy())

# plot the daily returns as a density plot

def plot_daily_returns_density(df: pd.DataFrame):
    df['daily_returns'] = df['close'].pct_change(fill_method=None) # type: ignore

    fig = px.density_contour(df, x="daily_returns", title='Daily Returns of Amazon Stock Price', labels={'daily_returns': 'Daily Returns', 'index': 'Date'}, histnorm='probability density')

    fig.update_layout(
        title="Distribution of Daily Returns of Amazon Stock Price",
        yaxis_title="Year",
        xaxis_title="Daily Returns",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
    )

    fig.show()

plot_daily_returns_density(df.copy())

# plot volatility and moving average

def plot_volatility_moving_average(df: pd.DataFrame):
    df['daily_returns'] = df['close'].pct_change(fill_method=None) # type: ignore
    df['volatility'] = df['daily_returns'].rolling(window=21).std()
    df['moving_average'] = df['close'].rolling(window=21).mean()

    # use log scale for better visualization
    df['volatility'] = np.log(df['volatility'])
    df['moving_average'] = np.log(df['moving_average'])

    fig = go.Figure()

    fig.add_trace(go.Scatter(x=df.index, y=df['volatility'], mode='lines', name='Volatility'))
    fig.add_trace(go.Scatter(x=df.index, y=df['moving_average'], mode='lines', name='Moving Average'))

    fig.update_layout(
        title="Amazon Stock Price Volatility and Moving Average",
        yaxis_title="Value",
        xaxis_title="Date",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
    )

    fig.show()

plot_volatility_moving_average(df.copy())

# plot the relationship between the volatility and the trading volume and calculate the correlation

def plot_volatility_trading_volume(df: pd.DataFrame):
    # set missing values to NaN
    df['volume'] = df['volume'].replace(0, np.nan)
    df['daily_returns'] = df['close'].pct_change(fill_method=None) # type: ignore
    df['volatility'] = df['daily_returns'].rolling(window=21).std()
    df['volume'] = df['volume'].rolling(window=21).mean()

    fig = px.scatter(df, x="volatility", y="volume", title='Volatility and Trading Volume', symbol=df.index.year) # type: ignore
    correlation = df['volatility'].corr(df['volume'])


    fig.update_layout(
        title="Amazon Stock Price Volatility and Trading Volume",
        yaxis_title="Volume",
        xaxis_title="Volatility",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
        legend_title_text=f"Correlation: {str(np.round(correlation, 4))}"
    )

    fig.show()

plot_volatility_trading_volume(df.copy())

# plot the autocorrelation of the daily returns

def plot_autocorrelation(df: pd.DataFrame):
    df['daily_returns'] = df['close'].pct_change(fill_method=None) # type: ignore

    fig = px.scatter(df, x="daily_returns", y="daily_returns", title='Autocorrelation of Daily Returns', symbol=df.index.year) # type: ignore

    fig.update_layout(
        title="Amazon Stock Price Autocorrelation of Daily Returns",
        yaxis_title="Daily Returns",
        xaxis_title="Daily Returns",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
    )

    fig.show()

plot_autocorrelation(df.copy())

# autocorrelation function and partial autocorrelation function

def plot_autocorrelation_function(df: pd.DataFrame):
    df['daily_returns'] = df['adj close'].pct_change()

    fig, ax = plt.subplots(2, 1, figsize=(15, 10))

    plot_acf(df['open'].dropna(), ax=ax[0])
    plot_pacf(df['open'].dropna(), ax=ax[1])

    plt.show()

plot_autocorrelation_function(df.copy())

# plot the seasonal decomposition

def plot_seasonal_decompose(
    result: DecomposeResult,
    dates: pd.Series = None, # type: ignore
    title: str = "Seasonal Decomposition",
):
    x_values = dates if dates is not None else np.arange(len(result.observed))
    return (
        sp.make_subplots(
            rows=4,
            cols=1,
            subplot_titles=["Observed", "Trend", "Seasonal", "Residuals"],
        )
        .add_trace(
            go.Scatter(x=x_values, y=result.observed, mode="lines", name="Observed"),
            row=1,
            col=1,
        )
        .add_trace(
            go.Scatter(x=x_values, y=result.trend, mode="lines", name="Trend"),
            row=2,
            col=1,
        )
        .add_trace(
            go.Scatter(x=x_values, y=result.seasonal, mode="lines", name="Seasonal"),
            row=3,
            col=1,
        )
        .add_trace(
            go.Scatter(x=x_values, y=result.resid, mode="lines", name="Residual"),
            row=4,
            col=1,
        )
        .update_layout(
            height=900,
            title=f"<b>{title}</b>",
            margin={"t": 100},
            title_x=0.5,
            showlegend=False,
        )
    )

# calculate the average number of trading days per year
trading_days_per_year = df.index.year.value_counts().mean() # type: ignore
print(f"Average number of trading days per year: {trading_days_per_year}")


decomposition = seasonal_decompose(df["adj close"], model='additive', period=int(np.round(trading_days_per_year, 0)), two_sided=False, extrapolate_trend=240)
fig = plot_seasonal_decompose(decomposition, dates=pd.Series(df.index) ,title="Seasonal Decomposition of Amazon Stock Price")
fig.show()

Average number of trading days per year: 240.42857142857142

# determine and visualize the heavy tails and kurtosis of the daily returns

def plot_heavy_tails_kurtosis(df: pd.DataFrame):
    df['daily_returns'] = df['adj close'].pct_change(fill_method=None) # type: ignore

    fig = px.histogram(df, x="daily_returns", title='Daily Returns of Amazon Stock Price', labels={'daily_returns': 'Daily Returns', 'index': 'Date'}, histnorm='probability density')

    kurtosis = df['daily_returns'].kurtosis()

    # data is heavy tailed if kurtosis > 3 
    fig.add_trace(go.Scatter(x=[0, 0], y=[0, 20], mode="lines", name="Kurtosis"))

    fig.update_layout(
        title="Amazon Stock Price Daily Returns",
        yaxis_title="Count",
        xaxis_title="Daily Returns",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
        legend_title_text=f"Kurtosis: {str(np.round(float(kurtosis), 4))}" # type: ignore
    )

    fig.show()

plot_heavy_tails_kurtosis(df.copy())

# investigate volatility

def plot_volatility(df: pd.DataFrame):
    df['daily_returns'] = df['adj close'].pct_change(fill_method=None) # type: ignore
    df['volatility'] = df['daily_returns'].rolling(window=21).std()

    fig = px.line(df, x=df.index, y="volatility", title='Volatility Clustering of Amazon Stock Price', labels={'volatility': 'Volatility', 'index': 'Date'})

    fig.update_layout(
        title="Amazon Stock Price Volatility",
        yaxis_title="Volatility",
        xaxis_title="Date",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
    )

    fig.show()

plot_volatility(df.copy())

# plot seasonal decomposition of the volatility

def plot_volatility_seasonal_decompose(df: pd.DataFrame):
    df['daily_returns'] = df['adj close'].pct_change()
    df['volatility'] = df['daily_returns'].rolling(window=21).std()

    trading_days_per_year = df.index.year.value_counts().mean() # type: ignore

    decomposition = seasonal_decompose(df["volatility"].dropna(), model='additive', period=int(np.round(trading_days_per_year, 0)), two_sided=False, extrapolate_trend=240)
    fig = plot_seasonal_decompose(decomposition, dates=pd.Series(df.index) ,title="Seasonal Decomposition of Amazon Stock Price Volatility")
    fig.show()

plot_volatility_seasonal_decompose(df.copy())

# volatility and daily returns

def plot_volatility_daily_returns(df: pd.DataFrame):
    df['daily_returns'] = df['adj close'].pct_change(fill_method=None) # type: ignore
    df['volatility'] = df['daily_returns'].rolling(window=21).std()

    fig = px.scatter(df, x="daily_returns", y="volatility", title='Volatility and Daily Returns', symbol=df.index.year) # type: ignore

    fig.update_layout(
        title="Amazon Stock Price Volatility and Daily Returns",
        yaxis_title="Volatility",
        xaxis_title="Daily Returns",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
    )

    fig.show()

plot_volatility_daily_returns(df.copy())

# investigate whether the autocorrelation of the daily returns of the DAX decay more slowly than in a random series

def compare_autocorrelation(df: pd.DataFrame):

    autocorr_dax = df['adj close'].pct_change(fill_method=None).autocorr() # type: ignore

    # Generate random series with the same length as daily returns
    random_series = np.random.randn(len(df))

    # Calculate autocorrelation of random series
    autocorr_random = pd.Series(random_series).autocorr()

    # Plot autocorrelation
    fig = go.Figure()

    fig.add_trace(
        go.Scatter(x=df.index, y=random_series, mode="lines", name="Random Series")
    )
    fig.add_trace(go.Scatter(x=df.index, y=df['close'].pct_change(fill_method=None), mode='lines', name='Amazon')) # type: ignore

    fig.update_layout(
        title="Autocorrelation of Daily Returns",
        yaxis_title="Value",
        xaxis_title="Date",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
    )

    fig.show()

    # Compare autocorrelation values
    if autocorr_dax > autocorr_random:
        print("The autocorrelation of the daily returns decays more slowly than in a random series.")
    else:
        print("The autocorrelation of the daily returns does not decay more slowly than in a random series.")

compare_autocorrelation(df.copy())

The autocorrelation of the daily returns does not decay more slowly than in a random series.

# investigate long memory 

def hurst_exponent(time_series):
    """Returns the Hurst Exponent of the time series"""
    lags = range(2, 100)
    tau = [np.sqrt(np.std(np.subtract(time_series[lag:], time_series[:-lag]))) for lag in lags]
    poly = np.polyfit(np.log(lags), np.log(tau), 1)
    return poly[0]*2.0


# Calculate the Hurst Exponent for the stock
hurst = hurst_exponent(df["adj close"].values)
print(f"Hurst Exponent: {hurst}")

Hurst Exponent: 0.4633310633830021

# Durbin-Watson test

def durbin_watson_test(df: pd.DataFrame):
    dw = durbin_watson(df['adj close'].pct_change(fill_method=None).dropna()) # type: ignore
    print(f"Durbin-Watson test statistic: {dw}")

# Call the function with your dataframe
durbin_watson_test(df.copy())

Durbin-Watson test statistic: 1.986993803449915

# investigate the leverage effect and the correlation between returns and volatility

def plot_leverage_effect_and_volatility_correlation(df: pd.DataFrame):

    # Calculate daily returns
    df['returns'] = df['close'].pct_change()

    # Calculate a rolling measure of volatility (using a 21-day moving window, typical of trading days in a month)
    df['volatility'] = df['returns'].rolling(window=21).std()

    # Calculate the correlation between returns and volatility
    correlation = df["returns"].corr(df["volatility"])

    # Calculate the leverage effect
    df['leverage_effect'] = df['returns'] * df['volatility'].shift(1)

    # Plot the leverage effect and the correlation between returns and volatility
    fig = go.Figure()

    fig.add_trace(go.Scatter(x=df.index, y=df['leverage_effect'], mode='lines', name='Leverage Effect'))
    fig.add_trace(go.Scatter(x=df.index, y=df['volatility'], mode='lines', name='Volatility'))

    fig.update_layout(
        title="Leverage Effect and Volatility Correlation",
        yaxis_title="Value",
        xaxis_title="Date",
        font=dict(family="Courier New, monospace", size=18, color="#333"),
        legend_title_text=f"Correlation: {str(np.round(correlation, 4))}"
    )

    fig.show()

plot_leverage_effect_and_volatility_correlation(df.copy())

# visualize missing values per weekday
def visualize_missing_values_per_weekday(df: pd.DataFrame):
    df['weekday'] = df.index.weekday # type: ignore

    missing_values_per_weekday = df.pivot_table(index='weekday', aggfunc=lambda x: x.isnull().sum()).sum(axis=1)

    fig = px.bar(x=missing_values_per_weekday.index, y=missing_values_per_weekday.values, title='Missing Values per Weekday')
    fig.update_layout(
        title="Missing Values per Weekday",
        yaxis_title="Count",
        xaxis_title="Weekday",
        font=dict(family="Courier New, monospace", size=18, color="#7f7f7f"),
    )
    # mask the x-axis label with weekday names
    fig.update_xaxes(
        tickmode="array",
        tickvals=[0, 1, 2, 3, 4],
        ticktext=[
            "Mon",
            "Tue",
            "Wed",
            "Thu",
            "Fri",
        ],
    )

    fig.show()


visualize_missing_values_per_weekday(df.copy())

# visualize missing values during the years 2014-2024

def visualize_missing_values_per_year(df: pd.DataFrame):
    missing_values_per_year = df.resample('YE').apply(lambda x: x.isnull().sum().sum()).sum(axis=1) # type: ignore

    fig = px.bar(x=missing_values_per_year.index, y=missing_values_per_year.values, title='Missing Values per Year') # type: ignore

    fig.update_layout(
        title="Missing Values per Year",
        yaxis_title="Count",
        xaxis_title="Year",
        font=dict(family="Courier New, monospace", size=18, color="#7f7f7f"),
    )
    fig.show()

visualize_missing_values_per_year(df.copy())

# Augmented Dickey-Fuller test

def get_stationarity(df: pd.DataFrame):

    # rolling statistics
    rolling_mean = df["adj close"].rolling(window=21).mean()
    rolling_std = df["adj close"].rolling(window=21).std()

    # rolling statistics plot
    fig = go.Figure()
    fig.add_trace(go.Scatter(x=df.index, y=df["adj close"], mode="lines", name="Original"))
    fig.add_trace(go.Scatter(x=df.index, y=rolling_mean, mode="lines", name="Rolling Mean"))
    fig.add_trace(go.Scatter(x=df.index, y=rolling_std, mode="lines", name="Rolling Std"))

    fig.update_layout(title="Rolling Mean & Standard Deviation", xaxis_title="Date", yaxis_title="Price")
    fig.show()

    # Dickey–Fuller test:
    result = adfuller(df["adj close"])
    print(f"ADF Statistic: {result[0]}")
    print(f"p-value: {result[1]}")
    print("Critical Values:")
    for key, value in result[4].items(): # type: ignore
        print("\t{}: {}".format(key, value))

# original data

get_stationarity(df.copy())

ADF Statistic: 0.8855301351858951
p-value: 0.9928985551526608
Critical Values:
	1%: -3.4313268266785926
	5%: -2.8619716758423386
	10%: -2.5669997774289297

# log data

get_stationarity(np.log(df.copy())) # type: ignore

ADF Statistic: -1.8812090334476543
p-value: 0.34095194783661675
Critical Values:
	1%: -3.4313268266785926
	5%: -2.8619716758423386
	10%: -2.5669997774289297

df_log = pd.DataFrame(np.log(df))
rolling_mean = df_log.rolling(window=21).mean()
df_log_minus_mean = df_log - rolling_mean
df_log_minus_mean.dropna(inplace=True)

get_stationarity(df_log_minus_mean)

ADF Statistic: -11.762490918590906
p-value: 1.1392262418639577e-21
Critical Values:
	1%: -3.4313297537494396
	5%: -2.8619729691501026
	10%: -2.5670004658825696

df_log_shift = df_log - df_log.shift()
df_log_shift.dropna(inplace=True)


get_stationarity(df_log_shift)

ADF Statistic: -13.980804374217193
p-value: 4.1809643708121255e-26
Critical Values:
	1%: -3.4313268266785926
	5%: -2.8619716758423386
	10%: -2.5669997774289297

# ACF and PACF plots

def plot_acf_pacf(df: pd.DataFrame):    
    fig, ax = plt.subplots(2, 1, figsize=(12, 8))
    plot_acf(df['adj close'].pct_change().dropna(), ax=ax[0])
    plot_pacf(df['adj close'].pct_change().dropna(), ax=ax[1])
    plt.show()

plot_acf_pacf(df.copy())

# train test split

def train_test_split(df: pd.DataFrame):
    # Split the data into a training and test set
    train_size = int(len(df) * 0.8)
    train, test = df.iloc[:train_size], df.iloc[train_size:]

    # Create a plot
    fig = go.Figure()

    # Original data
    fig.add_trace(go.Scatter(x=train.index, y=train['adj close'], mode='lines', name='Train'))
    fig.add_trace(go.Scatter(x=test.index, y=test['adj close'], mode='lines', name='Test'))

    fig.update_layout(title='Train Test Split', xaxis_title='Date', yaxis_title='Adj Close Price')
    fig.show()

    return train, test

train, test = train_test_split(df)

# plot PACF and ACF

def plot_acf_pacf(df: pd.DataFrame):
    
    fig, ax = plt.subplots(2, 1, figsize=(12, 8))
    plot_acf(df['adj close'], ax=ax[0], lags=100)
    plot_pacf(df['adj close'], ax=ax[1], lags=100)
    plt.show()	
   

plot_acf_pacf(df_log_shift)

#  ARIMA model

def arima_model(series, data_split, params, log):

    # log shift the series if log is True
    if log == True:
        series_dates = series.index
        series_log = np.log(series)
        series = series_log - series_log.shift().dropna()

    # create training and testing data sets based on user split fraction
    size = int(len(series) * data_split)
    train, test = series[0:size], series[size : len(series)]
    history = [val for val in train]
    predictions = []

    # creates a rolling forecast by testing one value from the test set, and then add that test value
    # to the model training, followed by testing the next test value in the series
    for t in range(len(test)):
        model = ARIMA(history, order=(params[0], params[1], params[2]))
        model_fit = model.fit()
        output = model_fit.forecast()
        predictions.append(output[0])
        obs = test[t]
        history.append(obs)

    test_dates = test.index

    # inverse log shift transformation
    if log == True:
        # series
        series = series + series_log.shift()
        series = pd.Series(np.exp(series), index=series_dates)
        series.dropna(inplace=True)

        # predictions
        predictions = predictions + series_log[size: len(series_log)].shift()
        predictions = pd.Series(np.exp(predictions), index=test_dates)
        predictions.dropna(inplace=True)

        # test
        test = test + series_log[size: len(series_log)].shift()
        test = pd.Series(np.exp(test), index=test_dates)
        test.dropna(inplace=True)

        # train
        train = train + series_log[0:size].shift()
        train = pd.Series(np.exp(train), index=series_dates)
        train.dropna(inplace=True)

    else:
        # creates pandas series with datetime index for the predictions
        predictions = pd.Series(predictions, index=test_dates)

    # generates plots to compare the predictions for out-of-sample data to the actual test values
    fig = go.Figure()
    fig.add_trace(go.Scatter(x=series.index, y=series.values, mode="lines", name="Original Data"))
    fig.add_trace(go.Scatter(x=test_dates, y=test, mode="lines", name="Test Data"))
    fig.add_trace(go.Scatter(x=test_dates, y=predictions, mode="lines", name="Predictions"))
    fig.update_layout(title="ARIMA Model", xaxis_title="Date", yaxis_title="Price")
    fig.show()


    # calculates root mean squared errors (RMSEs) for the out-of-sample predictions
    test_error = sqrt(mean_squared_error(predictions, test))
    print("Test RMSE: %.3f" % test_error)

    return predictions, test

# make predictions with ARIMA model

def make_predictions_arima():

    # define ARIMA parameters
    p = 0 # lag order (AR)
    d = 1 # degree of differencing (I)
    q = 0 # order of moving average (MA)

    # make predictions
    predictions, test = arima_model(
        df["adj close"], 0.8, [p, d, q], True
    )

    return predictions, test

make_predictions_arima()

Test RMSE: 4.073

(Date
 2018-10-09     91.976347
 2018-10-10     93.811931
 2018-10-11     82.362975
 2018-10-12     84.210199
 2018-10-15     93.032447
                  ...    
 2024-02-08    171.921263
 2024-02-09    169.152785
 2024-02-12    179.185128
 2024-02-13    170.255516
 2024-02-14    165.019438
 Name: adj close, Length: 1346, dtype: float64,
 Date
 2018-10-09     93.515999
 2018-10-10     87.762497
 2018-10-11     85.968002
 2018-10-12     89.430496
 2018-10-15     88.047501
                  ...    
 2024-02-08    169.839996
 2024-02-09    174.449997
 2024-02-12    172.339996
 2024-02-13    168.639999
 2024-02-14    170.979996
 Name: adj close, Length: 1346, dtype: float64)

# train LSTM model and make predictions including hyperparameter tuning


# convert an array of values into a matrix
def create_dataset(dataset, look_back):
    dataX, dataY = [], []
    for i in range(len(dataset) - look_back - 1):
        a = dataset[i : (i + look_back), 0]
        dataX.append(a)
        dataY.append(dataset[i + look_back, 0])
    return np.array(dataX), np.array(dataY)


def lstm_model(df: pd.DataFrame, log: bool):

    np.random.seed(123)

    # log transformation of data
    if log == True:
        series = pd.Series(np.log(df["adj close"]), index=df.index)

    series = df["adj close"] if log == False else series

    # Scale the data
    min_max_scaler = MinMaxScaler(feature_range=(0, 1))
    data_series = min_max_scaler.fit_transform(series.values.reshape(-1, 1)) # type: ignore

    # split into train and test sets
    train_size = int(len(data_series) * 0.8)
    test_size = len(data_series) - train_size
    train, test = data_series[0:train_size,:], data_series[train_size:len(data_series),:]

    # Create the dataset with a look back
    look_back = 3
    x_train, y_train = create_dataset(train, look_back)
    x_test, y_test = create_dataset(test, look_back)

    # Reshape the input for the LSTM
    x_train = np.reshape(x_train, (x_train.shape[0], 1, x_train.shape[1]))
    x_test = np.reshape(x_test, (x_test.shape[0], 1, x_test.shape[1]))

    # Create the model
    model = Sequential()
    model.add(LSTM(3, input_shape=(1, look_back)))
    model.add(Dense(1))
    model.compile(loss="mean_squared_error", optimizer="adam")

    # Early stopping
    early_stop = EarlyStopping(monitor="val_loss", patience=10, verbose=1)

    # Fit the model
    model.fit(
        x_train, y_train, epochs=50, batch_size=1, verbose=1, validation_data=(x_test, y_test), callbacks=[early_stop] # type: ignore
    )

    return model, x_train, y_train, x_test, y_test, min_max_scaler, data_series, look_back

# make predictions with LSTM model

def make_predictions_lstm(df: pd.DataFrame, log: bool):

    model, x_train, y_train, x_test, y_test, min_max_scaler, data_series, look_back = lstm_model(df, log=log)
    
    train_predict = model.predict(x_train)
    test_predict = model.predict(x_test)

    # invert predictions
    train_predict = min_max_scaler.inverse_transform(train_predict)
    y_train = min_max_scaler.inverse_transform([y_train]) # type: ignore
    test_predict = min_max_scaler.inverse_transform(test_predict)
    y_test = min_max_scaler.inverse_transform([y_test]) # type: ignore

    # inverse log transformation
    if log == True:
        train_predict = np.exp(train_predict)
        y_train = np.exp(y_train)
        test_predict = np.exp(test_predict)
        y_test = np.exp(y_test)

    print(y_train, train_predict, y_test, test_predict)
    # calculate root mean squared error
    trainScore = sqrt(mean_squared_error(y_train[0], train_predict[:, 0]))
    print("Train Score: %.2f RMSE" % (trainScore))
    testScore = sqrt(mean_squared_error(y_test[0], test_predict[:, 0]))
    print("Test Score: %.2f RMSE" % (testScore))

    # shift train predictions for plotting
    train_predictPlot = np.empty_like(data_series)
    train_predictPlot[:, :] = np.nan
    train_predictPlot[look_back : len(train_predict) + look_back, :] = train_predict

    # shift test predictions for plotting
    test_predictPlot = np.empty_like(data_series)
    test_predictPlot[:, :] = np.nan
    test_predictPlot[len(train_predict) + (look_back * 2) + 1 : len(data_series) - 1, :] = (
        test_predict
    )

    # plot baseline and predictions
    fig = go.Figure()
    fig.add_trace(go.Scatter(x=df.index, y=df["adj close"], mode="lines", name="Original"))
    fig.add_trace(
        go.Scatter(x=df.index, y=test_predictPlot[:, 0], mode="lines", name="Test Predictions")
    )
    fig.add_trace(
        go.Scatter(
            x=df.index, y=train_predictPlot[:, 0], mode="lines", name="Train Predictions"
        )
    )

    fig.update_layout(title="LSTM Model Predictions", xaxis_title="Date", yaxis_title="Price")
    fig.show()

make_predictions_lstm(df, log=True)

Epoch 1/50
5381/5381 [==============================] - 5s 767us/step - loss: 0.0025 - val_loss: 3.7931e-04
Epoch 2/50
5381/5381 [==============================] - 4s 724us/step - loss: 7.4084e-05 - val_loss: 5.5124e-04
Epoch 3/50
5381/5381 [==============================] - 4s 743us/step - loss: 6.9468e-05 - val_loss: 3.6853e-04
Epoch 4/50
5381/5381 [==============================] - 5s 848us/step - loss: 6.7479e-05 - val_loss: 1.7229e-04
Epoch 5/50
5381/5381 [==============================] - 4s 793us/step - loss: 6.1648e-05 - val_loss: 1.0957e-04
Epoch 6/50
5381/5381 [==============================] - 4s 827us/step - loss: 5.8408e-05 - val_loss: 1.6095e-04
Epoch 7/50
5381/5381 [==============================] - 4s 808us/step - loss: 5.6240e-05 - val_loss: 6.4835e-05
Epoch 8/50
5381/5381 [==============================] - 4s 780us/step - loss: 5.3056e-05 - val_loss: 2.3750e-04
Epoch 9/50
5381/5381 [==============================] - 4s 827us/step - loss: 5.1069e-05 - val_loss: 1.5572e-05
Epoch 10/50
5381/5381 [==============================] - 4s 782us/step - loss: 4.8641e-05 - val_loss: 1.9770e-04
Epoch 11/50
5381/5381 [==============================] - 4s 779us/step - loss: 4.6844e-05 - val_loss: 1.6463e-04
Epoch 12/50
5381/5381 [==============================] - 4s 810us/step - loss: 4.4906e-05 - val_loss: 2.2752e-05
Epoch 13/50
5381/5381 [==============================] - 4s 801us/step - loss: 4.4635e-05 - val_loss: 2.1662e-04
Epoch 14/50
5381/5381 [==============================] - 4s 782us/step - loss: 4.3641e-05 - val_loss: 1.8546e-05
Epoch 15/50
5381/5381 [==============================] - 4s 792us/step - loss: 4.2951e-05 - val_loss: 1.0961e-04
Epoch 16/50
5381/5381 [==============================] - 4s 778us/step - loss: 4.0883e-05 - val_loss: 1.4067e-05
Epoch 17/50
5381/5381 [==============================] - 4s 785us/step - loss: 4.0458e-05 - val_loss: 1.0433e-04
Epoch 18/50
5381/5381 [==============================] - 4s 780us/step - loss: 4.0881e-05 - val_loss: 1.1644e-05
Epoch 19/50
5381/5381 [==============================] - 4s 779us/step - loss: 3.9828e-05 - val_loss: 1.4781e-05
Epoch 20/50
5381/5381 [==============================] - 4s 763us/step - loss: 3.9470e-05 - val_loss: 1.1129e-05
Epoch 21/50
5381/5381 [==============================] - 4s 770us/step - loss: 3.8850e-05 - val_loss: 1.6517e-05
Epoch 22/50
5381/5381 [==============================] - 4s 764us/step - loss: 3.9082e-05 - val_loss: 9.7450e-05
Epoch 23/50
5381/5381 [==============================] - 4s 762us/step - loss: 3.6954e-05 - val_loss: 2.9335e-05
Epoch 24/50
5381/5381 [==============================] - 4s 783us/step - loss: 3.7303e-05 - val_loss: 1.3762e-05
Epoch 25/50
5381/5381 [==============================] - 4s 769us/step - loss: 3.7133e-05 - val_loss: 2.1501e-05
Epoch 26/50
5381/5381 [==============================] - 4s 769us/step - loss: 3.6615e-05 - val_loss: 1.1964e-05
Epoch 27/50
5381/5381 [==============================] - 4s 768us/step - loss: 3.6252e-05 - val_loss: 1.1051e-04
Epoch 28/50
5381/5381 [==============================] - 4s 765us/step - loss: 3.6021e-05 - val_loss: 1.4406e-05
Epoch 29/50
5381/5381 [==============================] - 4s 764us/step - loss: 3.5106e-05 - val_loss: 5.3155e-05
Epoch 30/50
5381/5381 [==============================] - 4s 766us/step - loss: 3.4825e-05 - val_loss: 1.4117e-05
Epoch 30: early stopping
169/169 [==============================] - 0s 488us/step
42/42 [==============================] - 0s 439us/step
[[8.1771000e-02 7.1354000e-02 6.9792000e-02 ... 9.8565498e+01
  9.7638000e+01 9.5471001e+01]] [[8.8182069e-02]
 [8.5102051e-02]
 [7.7914827e-02]
 ...
 [9.9628426e+01]
 [9.8628624e+01]
 [9.7546989e+01]] [[ 85.968002  89.430496  88.047501 ... 174.449997 172.339996 168.639999]] [[ 89.61806 ]
 [ 86.71331 ]
 [ 87.996315]
 ...
 [165.42377 ]
 [167.94719 ]
 [168.05927 ]]
Train Score: 0.40 RMSE
Test Score: 4.03 RMSE

# plot the model architecture

# def plot_model_architecture():
#     model = Sequential()
#     model.add(LSTM(4, input_shape=(1, 15)))
#     model.add(Dense(1))
#     plot_model(model, to_file="model.png", show_shapes=True)

# plot_model_architecture()

ARIMA vs LSTM for stock price analysis¶

Business Understanding¶

Data Understanding¶

Daily Returns¶

Volatility and Moving Average¶

Volatility and Trading Volume¶

Autocorrelation¶

Seasonal Decomposition¶

Heavy Tails and Kurtosis¶

Volatility Clustering¶

Fractional Integration and Long Memory¶

Leverage Effect¶

Missing Values¶

Data Preparation¶

Autocorrelation and Partial Autocorrelation¶

Modelling¶

ARIMA¶

LSTM¶

Evaluation¶

	open	high	low	close	adj close	volume
Date
2024-02-08	169.649994	171.429993	168.880005	169.839996	169.839996	42316500
2024-02-09	170.899994	175.000000	170.580002	174.449997	174.449997	56986000
2024-02-12	174.800003	175.389999	171.539993	172.339996	172.339996	51050400
2024-02-13	167.729996	170.949997	165.750000	168.639999	168.639999	56345100
2024-02-14	169.210007	171.210007	168.279999	170.979996	170.979996	42760600